It is totally grammatical and correct to say so, but in modern language you usually would say "я слышал, как она говорила...". I think there is some nuance here.
Consider the following setting. She is the factory manager. Now consider the phrases:
Я видел её говорившей с рабочими.
Я видел, как она говорила с рабочими.
Both can mean the same, you saw her talking to the workers. But the second one can also mean you saw how she was talking to the workers. Her manners, mimic, tone. If you want exclude this, you use the first one. It is momentary: this can mean you say her face was red, but you cannot say anything about time-prolonged details.
Now what about слышал instead of видел? Well, the same,
Я слышал её говорившей с рабочими.
means you heard some short moment of their conversation, by chance, like through a wall or by hearing their telephone call accidentally, but you cannot say in what manner and how she was speaking.
One more to note. Я слышал её говорившей can mean either once or several times, while я слышал, как она говорила can imply either only one (without referring to the manners) or referring to the manners (then likely not once).